Numerical solver uncertainty is high when the solutions of the differential equations of a model, computed with different numerical solvers, deviate from each other. Numerical solver uncertainty is a serious limiting factor of the simulation process and can lead to incorrect model predictions. This problem is especially critical because the correct solution trajectory of environmental models, often consisting of large systems of ODEs, is almost always unknown. The selection of the most appropriate solver, according to speed and correctness, is not a straightforward task and cannot be based on, for instance, literature. Moreover, with the advent of distributed computing, large amounts of data on previously run simulations are readily available. Analyzing these data can help automating the selection of the most appropriate solver. A new methodology for this automatic selection, based on the correctness of the solution from a repository of simulations, was developed and tested on a set of 16 models with different levels of complexity. This methodology is capable of finding deviating solutions when the model is computed with different solvers and settings, and shows that numerical solver uncertainty is quite common. A cluster of appropriate solvers, which are able to solve the model correctly, can be identified and the most efficient solver can be selected among them. This results in a reduction of the numerical solver uncertainty. On top of that, it was also possible to achieve a reduction of the computation time by a factor of 106, compared to slow, but undoubtedly correct solvers.
Research Article|March 01 2009
Automatic numerical solver selection from a repository of pre-run simulations
Peter A. Vanrolleghem
Peter A. Vanrolleghem
1BIOMATH, Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, Ghent, B-9000, Belgium
2modelEAU, Département de génie civil, Pavillon Pouliot, Université Laval, Québec, G1K 7P4, QC, Canada
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Water Sci Technol (2009) 59 (5): 893-906.
Petra Claeys, Peter A. Vanrolleghem, Bernard De Baets; Automatic numerical solver selection from a repository of pre-run simulations. Water Sci Technol 1 March 2009; 59 (5): 893–906. doi: https://doi.org/10.2166/wst.2009.034
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